Theorem bi1imp 42101

Description: Importation inference similar to imp 407, except the outermost implication of the hypothesis is a biconditional. (Contributed by Alan Sare, 6-Nov-2017.)

Hypothesis

Ref	Expression
bi1imp.1	⊢ (𝜑 ↔ (𝜓 → 𝜒))

Assertion

Ref	Expression
bi1imp	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem bi1imp

Step	Hyp	Ref	Expression
1		bi1imp.1	. . 3 ⊢ (𝜑 ↔ (𝜓 → 𝜒))
2	1	biimpi 215	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	2	imp 407	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ↔ wb 205   ∧ wa 396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397

This theorem is referenced by: (None)